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A Characterization of Individualization-Refinement Trees

Authors Markus Anders, Jendrik Brachter, Pascal Schweitzer

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ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Trees
Keywords
  • individualization refinement algorithms
  • backtracking trees
  • graph isomorphism

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Abstract

Individualization-Refinement (IR) algorithms form the standard method and currently the only practical method for symmetry computations of graphs and combinatorial objects in general. Through backtracking, on each graph an IR-algorithm implicitly creates an IR-tree whose order is the determining factor of the running time of the algorithm.
We give a precise and constructive characterization which trees are IR-trees. This characterization is applicable both when the tree is regarded as an uncolored object but also when regarded as a colored object where vertex colors stem from a node invariant. We also provide a construction that given a tree produces a corresponding graph whenever possible. This provides a constructive proof that our necessary conditions are also sufficient for the characterization.

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Markus Anders, Jendrik Brachter, and Pascal Schweitzer. A Characterization of Individualization-Refinement Trees. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ISAAC.2021.24

Author Details

Markus Anders
  • TU Darmstadt, Germany
Jendrik Brachter
  • TU Darmstadt, Germany
Pascal Schweitzer
  • TU Darmstadt, Germany

Funding

Supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (EngageS: grant No. {820148}).

References

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